JPH0528280A - Light beam tracking method - Google Patents

Abstract

PURPOSE:To realize high-speed light beam tracking processing at the time of generating an image by tracking a light beam by using object definition data of graded tree structure. CONSTITUTION:Graded object definition data of tree structure is given with regard to the object space of an image generation object as a given figure. A partial tree consisting an object projected on a small space 2' is dynamically prepared at the respective small spaces of an image face (screen) 2 by using object definition data graded into the tree structure. Then, a beam is tracked at the respective small spaces of the image face 2 by using the partial tree, the values of the respective picture elements of the small spaces are obtained and the image is generated. At this time, a partial tree is furthermore prepared and light beam is similarly tracked with regard to reflection and refraction light. The processing is repeated with regard to the respective small spaces.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to the field of image generation by a ray tracing method, and more particularly to a high speed processing method of the ray tracing method.

[0002]

2. Description of the Related Art An image generation method using a ray tracing method traces a ray from the viewpoint toward the object, and if the ray intersects the object, the brightness of the object at that point is obtained and the image plane (screen) is displayed. This is a method of projecting and generating an image, but its problem is that the calculation takes a considerable amount of time. Most of this calculation time is spent on the intersection determination between the ray and the object. Therefore, a data structure and an algorithm aiming to reduce the number of intersection determinations are proposed.

The essence of speeding up the ray tracing algorithm is
In other words, for each pixel on the image plane, the object projected on that pixel can be efficiently obtained. For that purpose, various speed-up techniques have been proposed conventionally. When the conventional methods are classified, data hierarchy and Boundind
The use of Volume (BV) and the use of Ray coherency are roughly divided.

It is well known how to reduce the number of intersection determinations by hierarchizing object definition data and using BV.
Hierarchization using an Octree or Constructive Solid Geometry (CSG) model is one example. In these models, for each node of a hierarchical tree, a BV that includes all the object limits of leaf nodes that are descendants of the node is set as necessary. By performing the intersection determination on these BVs, the number of intersection calculations can be significantly reduced. Based on the fact that "the smaller the volume of BV, the smaller the number of rays that intersect the object", studies are being made to efficiently find a BV whose volume is as small as possible.

On the other hand, Arvo et al. Classify rays according to the viewpoint and direction, group similar rays, and obtain candidates for objects that intersect with these rays, thereby obtaining intersection candidates by obtaining candidate objects for intersection determination. We have proposed a method to reduce the number of candidate objects (Arvo J., Kirk).
D .: “Fast Ray Tracing by ray Classicificatio
n ”, Comput. Graphics, Vol. 21. No. 4, pp. 55
-64, Jul. 1987). This method can efficiently classify candidate objects, and thus has a large effect of speeding up the ray tracing method.

[0006]

Although any of the above methods has a great effect on speeding up, it is necessary to realize higher speed processing. In the conventional method, since the ray tracing is performed using the hierarchical tree structure as it is, at least the intersection determination calculation of the tree depth is necessary, which is a bottleneck for reducing the amount of calculation.

SUMMARY OF THE INVENTION An object of the present invention is to provide a ray tracing method which has an extremely high speed-up effect in a method of generating an image while tracing a ray to obtain the brightness of an object.

[0008]

In order to achieve the above object, a method of generating an image while tracing a ray from a viewpoint toward a direction of an object to obtain the brightness of the object is a tree structure. Using the object definition data layered into
A feature is that, for each small area of the image plane, a partial tree composed of an object projected on the small area is dynamically created, and ray tracing is performed using the partial tree.

According to a second aspect of the invention, the bounding volumes set for the respective nodes of the subtree are dynamically rearranged in order of decreasing distance from the viewpoint with respect to the ray to be traced,
It is characterized in that the subtrees are searched in the ascending order of distance.

According to a third aspect of the present invention, it is determined whether or not the objects projected on the small area are occupied by the same object, and when the objects are occupied by the same object, the subtree search in the small area is performed. It is characterized in that it is omitted.

According to the fourth aspect of the present invention, for reflected / refracted light rays, a pyramid or a cone including the majority of the light rays reflected / refracted from the small area is formed for each small area and included in the pyramid or the cone. It is characterized in that a subtree consisting of objects is dynamically created and ray tracing is performed using the subtree.

[0012]

In the present invention, the number of objects projected onto the small area of the image plane (screen) is reduced by dynamically creating a subtree from the given object definition data of the tree structure and reducing the depth of the tree. Therefore, the number of intersection determinations can be reduced. Furthermore, by sorting by the distance from the viewpoint at each node level of the subtree, and by adding the uniformity test of the objects in the small area, the candidate objects that intersect the ray can be narrowed down very efficiently, and high-speed processing is possible. It will be possible. For reflected / refracted light, a subtree is further created for each small area, and ray tracing is performed using the subtree, so that not only the primary ray but also the ray traced image by reflected / refracted light is simultaneously displayed. Is generated.

[0013]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described below with reference to the drawings.

FIG. 1A shows the principle of the ray tracing method of the present invention. In FIG. 1, 1 is an eye (viewpoint), 2 is an image plane (screen), 3 is an object space, and 4 is a light ray.
There are many objects (primitives) Pi in the object space 3 of the image generation target. This object space 3 is hierarchically divided until each subspace contains one primitive,
For each subspace, a bounding volume (BV) that contains all the primitives that enter the space is created, and the definition data of the object is hierarchized. The hierarchical structure of the object definition data corresponding to the object space 3 in FIG.
It shows in (b). Here, the circles are nodes, and the node BVi corresponding to the bounding volume (BV) is
The node Pi that represents the coordinates of the BV and corresponds to the object (primitive) represents the equation, surface attribute, center position, and the like of the object. The layering of the object definition data will be described later.

According to the present invention, the image plane (screen) 2 is divided into a large number of small areas 2 ', and the intersection judgment is performed for each small area by referring to the hierarchical structure of the object definition data given in advance. A subtree consisting of objects projected onto the small area is dynamically created. Then, ray tracing is performed using this subtree, the brightness of the object projected on each small area is obtained for each small area, and the brightness is plotted on the image plane 2 (rendering). At this time, if there is a reflected ray (refraction ray) 4 ', a partial tree corresponding to it is also dynamically generated, ray tracing is further performed using this partial tree, and the image of the reflection (refraction) object is also included in the corresponding small area. Overlay and plot. The above process is repeated for each small area.

2 and 3 are flowcharts of an embodiment of the image generation processing by the ray tracing method of the present invention, and FIG. 4 is an explanatory view of dividing the image plane (screen) into small areas.

In FIG. 2, the object definition data hierarchized in a tree structure is used to determine the intersection of a ray and a BV or an object (primitive) for each small area 2'of the image plane 2, and the small area is defined. This is the process until the subtree is created. In this embodiment, the processing is performed for each small area of the image plane 2 in the horizontal direction from left to right and in the vertical direction from top to bottom. FIG. 4 shows a part in which ray tracing is performed using the created subtree (also tracing of catadioptric light is performed), and rendering of a primitive projected on one small area is performed. The rendering is repeated for each small area.

The processes shown in FIGS. 2 and 3 are actually carried out on a computer. less than,
The main processing will be described in detail.

Hierarchization of Object Definition Data Space division methods include uniform division and non-uniform division.
Which one should be selected should be decided by combining the cost of creating the data structure and the cost of ray tracing, but since it generally depends on the data, good or bad cannot be generally stated.
Here, consider the latter division. The latter division has a tree structure. Specifically, the space is divided into k subspaces, and the object (primitive) is divided into respective subspaces. If the primitive spans a subspace, put it in one of the subspaces. For example, put it in a subspace that shares the largest volume. This division continues recursively until each subspace contains one primitive. When the division is over,
For each subspace, create a bounding volume (BV) that contains all the primitives that enter that space.
This division creates a k-ary tree data structure. It is necessary to determine the value of k.

If the trees are balanced, the following can be determined. Now, assume that hierarchization is performed using a k-ary tree as shown in FIG. BV is set to each intermediate node of this tree. Ray tracing using this tree, for each ray,
First, B set for all child nodes of the root node
Crossing judgment with V is performed. Then, one of these nodes is selected in some way, and intersection determination is performed for all its child nodes. If the intersection determination proceeds to the leaf node without backtracking, the number N of intersection determinations for that ray is

[Equation 1] Becomes Here, n is the number of primitives.

K which minimizes N when n is fixed is k
= E (base of natural logarithm). Since k is an integer, k = 3 actually gives the minimum value of N. Then k = 2,4
Becomes 2 and 4 give the same value. Therefore, it is effective to have a ternary tree or 2 (4) -ary tree structure. That is, if backtracking does not occur or a node selection method with very few occurrences is given, 3 or 2
(4) Hierarchization by using a progressive tree is advantageous. Below, a binary tree is used in consideration of affinity with other speed-up techniques. Figure 1
(B) is a simple example of a binary tree.

It is desirable to set the shape of the BV and the intersection determination BV so that the volume is as small as possible, but it is necessary to set the intersection determination cost in consideration. Now, let us consider a tree structure in which a BV is set in each node as shown in FIG. 6A, and assume that the projection on the image plane (screen) is as shown in FIG. 6B. Here, the projected area is represented by Si. When the ray hits the node n1, the intersection with the BV of the child node is determined. Therefore, n1
Under the condition that the ray hits, the time T required to determine the intersection with the child node is

[Equation 2] Becomes Here, C ₁ is the intersection determination cost with the BV set to n1.

If there is no backtrack, this formula holds for each node of the tree to be searched. In this case, from this equation, the total calculation time can be reduced if the intersection determination cost is low even if a simple shape BV is used.
(Even if the projected area is doubled, if the cost is half, the calculation time is the same.) Below, the axis as BV (world coordinates)
Use a rectangular parallelepiped.

Dynamic Partial Tree It is wasteful to perform ray tracing for each pixel on the image plane (screen) using the tree given first. This is because the number of primitives projected on the small area of the image plane is limited. Therefore, it is possible to dynamically create a subtree for each small area from a given tree and perform ray tracing using the partial tree in the small area. Here, the primary ray (ray traced from the viewpoint) will be described. If a small area is a square area or a rectangular area, a subtree is created from a primitive that intersects with or intersects a pyramid formed by the four corner points of the viewpoint and the area (the bundle of rays within this pyramid is Called luminous flux). It is disadvantageous if this production cost is high, but it is actually low from the following consideration.

(A) Pyramid creation The pyramid is composed of four planes, but it is not necessary to obtain these planes for each small area. In the case of pyramids for small areas arranged in the horizontal direction on the image plane, the planes in the horizontal direction (the upper and lower surfaces are the same) are common to both pyramids (for example, HF ₀ and HF _{1 in} FIG. 4). . In the small regions arranged in the vertical direction, the same relationship holds for the vertical planes (VF ₀ and VF _{1 in} FIG. 4). Also, adjacent surfaces can be shared. The inside of the pyramid can be uniquely defined by setting the half space in the normal direction of the plane to the outside and the opposite side to the inside. Therefore, the size of the image plane is n × n, and the size of the small area is m × n.
If m, the total number of planes required is 2 (n / m + 1)
Becomes

(B) Four flags are given to each node of the dynamic subtree creation tree. Each flag corresponds to the surface of the pyramid and indicates whether the BV or primitive corresponding to the node is inside, outside or intersects with the surface. The flag of each node is set starting from the root node of the tree. This is obtained by the intersection determination in FIG. At this time, if it is inside or outside the surface at a certain node, it is not necessary to set a flag for the surface below the child node. This is clear from the property of BV.

If the image generation is performed in the small areas and then in the horizontal small areas, the flag for the horizontal plane can be commonly used for all the small areas arranged in the horizontal direction. Further, with respect to the flag setting for the vertical face, unnecessary inside / outside determination can be omitted by referring to the flag for the horizontal plane. FIG. 2 shows such a process. A subtree is constructed with reference to these flags.
That is, B that intersects with the pyramid or is included in the pyramid.
Construct a subtree consisting only of V and primitives.
At this time, the optimization shown in FIG. 7 is also performed. Since the effect of pruning works as apparent from the method of making, the cost of making a subtree can be kept low. The subtree creation method described here can be similarly applied to secondary rays (reflected / refracted light).

Based on the fact that a primitive closer to the viewpoint than the sorting is projected on the image plane and the BV containing the primitive is often closer to the viewpoint than the BV containing other primitives. Sorting by distance from the viewpoint at each level. That is, the BV of a certain node
When the ray intersects and it becomes necessary to make an intersection determination for the child node, the child nodes are rearranged in the order of closer distance from the viewpoint. This is done for each ray.

In the depth-first tree search, if sorting is performed at each level of the tree, as shown in FIG. 8, the distance from the viewpoint of the primitive obtained by searching a certain child node or less. Is closer than the distance from the viewpoint of the BV set for the next child node, the search below the child node is unnecessary. In this way, pruning using sorting can be performed.

If a binary tree is used, the sorting of the child nodes needs only one comparison, which is extremely efficient. Here is the reason for using the binary tree.

Uniformity test in small area If it is known in some way that the small area is a projected image of the same primitive, the primitive may be rendered in this area. This means that it is not necessary to search for a tree in the area, which has a great effect on speeding up. Also, this test is required to be as simple as possible.

Here, the following simple test method is performed. Ray tracing is performed for points at the four corners of the small area. At this stage, the subtree is sorted by the ray traced fourth. Now, assume that the primitives at the four corners are the same. Let it be P. At this time, it suffices to check that there is no other primitive closer to the viewpoint than the primitive P in the small area. Subtree is Left-most Depth-F
Search on irst to find primitive Q. Q is on the far left of the tree. Due to the way the tree is constructed, Q is closer to the viewpoint than P. If P and Q are not the same, this area is not uniform. It is assumed that P and Q are the same. At this time P
Examine the younger brother node of. The younger brother node is either primitive or BV is set. Let it be R. R
Checks if it intersects the 4th traced ray. this is,
Just look at the flags. If they intersect, the area is uniform. Otherwise, it is assumed to be uneven.

This test does not give a judgment that it is always uniform when it is uniform in the area. However, when it is judged that the area is uniform, it means that there is no other primitive before the primitive P. Guaranteed. An example thereof is shown in FIGS. FIG. 9A shows an example in which it is determined to be non-uniform, and FIG. 9B shows an example in which it is determined to be non-uniform although it is originally uniform. FIG. 10 is an example in which it is determined to be uniform. In the case of FIG. 10, there is no other primitive in front of the primitive, but there is a part that is not a primitive in the small area, so that the part is traced using a subtree. When there are no primitives at the four corners, the condition for no primitives in the area is that the subtree is empty.

When the area is not uniform, the area is divided into two and the uniformity test is performed. This is repeated recursively as long as the size of the area does not fall below the threshold.

Tracing of Reflected / Refracted Light Beam A light beam passing through a rectangular area of the screen can be represented by a truncated pyramid, and the methods described so far can be applied. However, it is difficult to accurately describe general reflected / refracted light beams. Here, the reflected / refracted light beam is approximated, and an approximate bounding volume (hereinafter referred to as PBV) of the light beam including it is obtained. For an approximate PBV, a subtree is obtained and a uniformity test is performed. For each reflected / refracted ray, it is checked whether or not it is included in the approximate PBV obtained in, and if it is included, the result obtained in is used. Take the approach. The problem here is how to obtain the approximate PBV.

It is known that the paraxial approximation is effective as an approximation of reflection and refraction when the spread of the light flux is small (Shinya M., Takahashi T., Naito S .: "Prin.
cipesand Applications of Pencil Tracing ”, Com
put. Graphics, Vol.21, No.4, pp.45-54,
Jul. 1987). Therefore, using the paraxial approximation, the approximation P
Let's get the BV.

According to paraxial theory, one point (for example, viewpoint)
The paraxial light flux emitted from has two focal lines, and the directions of the focal lines are orthogonal to each other. That is, as shown in FIG. 11, the paraxial light flux is described as a region surrounded by a set of two planes having intersecting lines orthogonal to each other. Therefore, it is reasonable to use this area as an approximation of the luminous flux. However, the actual light flux is not an ideal approximate light flux, and many light rays are projected outside the area of the approximate light flux (FIG. 12).
(A)). Therefore, it is considered to find the PBV of the approximate light flux based on the light rays at the four corners of the light flux. There are many methods for obtaining this, but as a simple method, there is a method in which the largest angle of the deflection angles of the light rays at the four corners is used as the divergence angle of PBV. Figure 1
In the two-dimensional example shown in 2 (a), | θ1 |> | θ2 |
Therefore, the PBV as shown in FIG. 12B is obtained.
Specifically, the approximate ray PBV is obtained by the following procedure.

The reflected / refracted light rays i corresponding to the four corners of the small area of the screen are obtained by Snell's law. The average of the four rays obtained is taken as the axial ray. An appropriate ray coordinate x-y-z with the axial ray as the z-axis is obtained. However, the origin is set so that the one in front of the starting points of the four rays is z = 0. The starting points and directions of the four rays are transformed into a ray coordinate system, and the intersection points r _i = (r _xi , r _yi ) with the plane of z = 0 and the directions S _i = (S _ix , S _iy ) = (( dx / dz) _i , (dy
/ Dz) _i ). r _xmax = max (r _xi ), r _xmin = min (r _xi ), r _ymax
= Max ( _ry ), _rymin = min ( _ry ) and _sxmax = max
(| S _xi |), _symax = max (| s _yi |) is _calculated . The four planes to be obtained are given by the following equations.

[Equation 3] Although the x and y axes can be set arbitrarily, it is efficient to set them along the focal line direction.

This approximate PBV creating method is the simplest, and various modifications can be considered. The following can be considered as an example. It is also possible to obtain not only the light rays at the four corners but also the reflected / refracted light rays corresponding to all the pixels, and bounce them by the same method. This ensures that all rays to be traced are included in the PBV. This PBV includes a useless space when the light flux converges after being reflected (FIG. 13A). Therefore, the convergent light flux is bounded by two near-flux light fluxes as shown in FIG.

If the small area is uniform, a subtree is formed by PBV that looks into the light source from the four corners, and the shadow is tested. If the rays are parallel rays, the PBV becomes a prism. Since the direction vector of each surface forming the prism is constant regardless of location, the cost of forming the prism is small.

Next, the following algorithm is prepared to show the speed-up effect of the present invention. Below, the algorithm of A assumes the use of a binary tree structure. A1: Only BV is used. A2: Use BV and sorting. A2 ': Use subtree and BV. A3: Use subtree, BV, and sorting. A4: Use all. (A3 + uniformity test) The Arvo method is used as a comparison target. B1: Arvo algorithm

An example of the effect of speeding up the following five types of data will be shown. 1) Regularly arrange spheres with a constant radius in the space. Prepare spheres with two different radii. (2 types) 2) Randomly arrange spheres having a random radius in the space. (1 type) 3) 1 and 8 teapots (2 types)

An example of image generation is shown in FIGS. The number of pixels of the generated image is 512 × 512. Also,
The small area is basically 8 × 8 in size. The total number of primitives in FIGS. 14 to 16 is 512, and FIG.
That of FIG. 18 is 522 and 4416 respectively. B
V uses a rectangular parallelepiped along the axis.

The image generation time and the number of intersection determinations are shown in Tables 1 and 2.
Shown in.

[Table 1]

[Table 2]

From these results, the speed-up effect of the algorithm of the present invention can be seen as follows. (a) Algorithm A4 generates an image in the shortest time with any data. Also, comparing A3 and B1,
The image generation time of A3 is shorter than that of B1. (b) From the comparison between A1 and A2 ', the effect that the subtree contributes to the speedup is extremely high. This is, as shown in Table 2, A
This is an effect obtained because the number of 2'crossing decision circuits is significantly reduced. (c) The effect of the region uniformity test depends on the size of the primitive. Even if the uniformity region is small as shown in FIG. 15, the speed-up effect can be obtained. (d) In A2, as can be seen by comparing the BV and primitive intersection determination circuits, it can be seen that backtracking during tree search is extremely small by using sorting.

[0046]

As described above, according to the first aspect of the invention, a scene tree is dynamically created from the given object definition data having a tree structure, and the depth of the tree is made shallow, whereby the image plane ( The number of objects projected on a small area of
The number of intersection determinations can be reduced.

According to the second and third aspects of the present invention, by sorting by the distance from the viewpoint at each node level of the subtree, and by adding the uniformity test of the objects in the small area, the narrowing down of the candidate objects intersecting the ray is performed. Can be done very efficiently,
Further, high speed processing becomes possible.

According to the fourth aspect of the present invention, regarding reflected / refracted light, a subtree is further formed for each small region, and ray tracing is performed using the subtree, so that not only the primary ray but also the reflected / refracted light is reflected. An image of ray tracing by light is also generated at the same time.

[Brief description of drawings]

FIG. 1 is a principle diagram of a ray tracing method of the present invention.

FIG. 2 is a processing flow chart of an embodiment of the present invention.

FIG. 3 is a subsequent process flow diagram of the present invention.

FIG. 4 is a diagram showing division of an image surface (screen).

FIG. 5 is a diagram showing a general example of a tree structure of object definition data.

FIG. 6 Bounding volume (BV) of object space
It is a figure which shows the relationship between the projected area and intersection determination cost.

FIG. 7 is a diagram showing optimization of a subtree.

FIG. 8 is an explanatory diagram of sorting of partial trees.

FIG. 9 is a diagram showing an example of a small area uniformity test.

FIG. 10 is a diagram showing a test example of uniformity of small areas in the same manner.

FIG. 11 is an explanatory diagram of paraxial light flux.

FIG. 12: Bounding volume (PBV) of luminous flux
It is a figure which shows the structural example.

FIG. 13 is a diagram showing an improved example of PBV.

FIG. 14 is an example of image generation.

FIG. 15 is an example of image generation.

FIG. 16 is an example of image generation.

FIG. 17 is an example of image generation.

FIG. 18 is an example of image generation.

[Explanation of symbols]

1 viewpoint (eye) 2 Image plane (screen) 2'small area 3 Target object space 4 rays 4'reflected ray BV bounding volume P object (primitive)

Claims (4)

[Claims] 1. A method of generating an image while tracing a light ray from a viewpoint toward a direction of an object to obtain the brightness of the object, wherein object definition data layered in a tree structure is used, and each small area of an image plane is used. In addition, a ray tracing method is characterized in that a partial tree made up of objects projected onto the small area is dynamically created, and ray tracing is performed using the partial tree. 2. The subtrees are dynamically searched for in the order of closer distances from the viewpoint with respect to the ray to be traced, and the bounding volumes set in the nodes of the subtrees are dynamically rearranged. The ray tracing method according to claim 1. 3. A method for determining whether or not an object projected on a small area is occupied by the same object, and when the object is occupied by the same object, a search for a subtree within the small area is omitted. The ray tracing method according to claim 1 or 2. 4. With respect to reflected / refracted light rays, for each small area, a pyramid or cone containing the majority of the light rays reflected / refracted from the small area is formed, and a portion consisting of an object included in the pyramid or cone. The ray tracing method according to claim 1, 2 or 3, wherein a tree is dynamically created and ray tracing is performed using the subtree.